Search

Imaging is central to gaining microscopic insight into physical systems, and new microscopy methods have always led to the discovery of new phenomena and a deeper understanding of them. Ultracold atoms in optical lattices provide a quantum simulation platform, featuring a variety of advanced detection tools including direct optical imaging while pinning the atoms in the lattice 1,2 . However, this approach suffers from the diffraction limit, high optical density and small depth of focus, limiting it to two-dimensional (2D) systems. Here we introduce an imaging approach where matter wave optics magnifies the density distribution before optical imaging, allowing 2D sub-lattice-spacing resolution in three-dimensional (3D) systems. By combining the site-resolved imaging with magnetic resonance techniques for local addressing of individual lattice sites, we demonstrate full accessibility to 2D local information and manipulation in 3D systems. We employ the high-resolution images for precision thermodynamics of Bose-Einstein condensates in optical lattices as well as studies of thermalization dynamics driven by thermal hopping. The sub-lattice resolution is demonstrated via quench dynamics within the lattice sites. The method opens the path for spatially resolved studies of new quantum many-body regimes, including exotic lattice geometries or sub-wavelength lattices 3-6 , and paves the way for single-atom-resolved imaging of atomic species, where efficient laser cooling or deep optical traps are not available, but which substantially enrich the toolbox of quantum simulation of many-body systems., (© 2021. The Author(s).)

Integer-valued topological indices, characterizing nonlocal properties of quantum states of matter, are known to directly predict robust physical properties of equilibrium systems. The Chern number, e.g., determines the quantized Hall conductivity of an insulator. Using non-interacting fermionic atoms in a periodically driven optical lattice, here we demonstrate experimentally that the Chern number determines also the far-from-equilibrium dynamics of a quantum system. Extending a respective proposal to Floquet systems, we measure the linking number that characterizes the trajectories of momentum-space vortices emerging after a strong quench. We observe that it directly corresponds to the ground-state Chern number. This one-to-one relation between a dynamical and a static topological index allows us to experimentally map out the phase diagram of our system. Furthermore, we measure the instantaneous Chern number and show that it remains zero under the unitary dynamics.

Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due to the momentum-dependent coupling of the two sublattice states, which gives rise to a pseudospin texture. The topological defects appear as vortices in the azimuthal phase of this pseudospin texture. Here, we demonstrate a complete measurement of the azimuthal phase in a hexagonal optical lattice employing a versatile method based on time-of-flight imaging after off-resonant lattice modulation. Furthermore, we map out the merging transition of the two Dirac points induced by beam imbalance. Our work paves the way to accessing geometric properties in optical lattices also with spin-orbit coupling and interactions.

Topological properties lie at the heart of many fascinating phenomena in solid-state systems such as quantum Hall systems or Chern insulators. The topology of the bands can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Using fermionic ultracold atoms in a hexagonal optical lattice, we engineered the Berry curvature of the Bloch bands using resonant driving and show a full momentum-resolved measurement of the ensuing Berry curvature. Our results pave the way to explore intriguing phases of matter with interactions in topological band structures., (Copyright © 2016, American Association for the Advancement of Science.)

Phase transitions are ubiquitous in our three-dimensional world. By contrast, most conventional transitions do not occur in infinite uniform low-dimensional systems because of the increased role of thermal fluctuations. The crossover between these situations constitutes an important issue, dramatically illustrated by Bose-Einstein condensation: a gas strongly confined along one direction of space may condense along this direction without exhibiting true long-range order in the perpendicular plane. Here we explore transverse condensation for an atomic gas confined in a novel trapping geometry, with a flat in-plane bottom, and we relate it to the onset of an extended (yet of finite-range) in-plane coherence. By quench crossing the transition, we observe topological defects with a mean number satisfying the universal scaling law predicted by Kibble-Zurek mechanism. The approach described can be extended to investigate the topological phase transitions that take place in planar quantum fluids.

We create supercurrents in annular two-dimensional Bose gases through a temperature quench of the normal-to-superfluid phase transition. We detect the magnitude and the direction of these supercurrents by measuring spiral patterns resulting from the interference of the cloud with a central reference disk. These measurements demonstrate the stochastic nature of the supercurrents. We further measure their distribution for different quench times and compare it with predictions based on the Kibble-Zurek mechanism.

We present a general "fit-free" method for measuring the equation of state (EoS) of a scale-invariant gas. This method, which is inspired from the procedure introduced by Ku et al. [Science 335, 563 (2012)] for the unitary three-dimensional Fermi gas, provides a general formalism which can be readily applied to any quantum gas in a known trapping potential, in the frame of the local density approximation. We implement this method on a weakly interacting two-dimensional Bose gas across the Berezinskii-Kosterlitz-Thouless transition and determine its EoS with unprecedented accuracy in the critical region. Our measurements provide an important experimental benchmark for classical-field approaches which are believed to accurately describe quantum systems in the weakly interacting but nonperturbative regime.

Quantum phases of matter are characterized by the underlying correlations of the many-body system. Although this is typically captured by a local order parameter, it has been shown that a broad class of many-body systems possesses a hidden nonlocal order. In the case of bosonic Mott insulators, the ground state properties are governed by quantum fluctuations in the form of correlated particle-hole pairs that lead to the emergence of a nonlocal string order in one dimension. By using high-resolution imaging of low-dimensional quantum gases in an optical lattice, we directly detect these pairs with single-site and single-particle sensitivity and observe string order in the one-dimensional case.

We experimentally demonstrate coherent light scattering from an atomic Mott insulator in a two-dimensional lattice. The far-field diffraction pattern of small clouds of a few hundred atoms was imaged while simultaneously laser cooling the atoms with the probe beams. We describe the position of the diffraction peaks and the scaling of the peak parameters by a simple analytic model. In contrast to Bragg scattering, scattering from a single plane yields diffraction peaks for any incidence angle. We demonstrate the feasibility of detecting spin correlations via light scattering by artificially creating a one-dimensional antiferromagnetic order as a density wave and observing the appearance of additional diffraction peaks., (© 2011 American Physical Society)

Ultracold atoms in optical lattices provide a versatile tool with which to investigate fundamental properties of quantum many-body systems. In particular, the high degree of control of experimental parameters has allowed the study of many interesting phenomena, such as quantum phase transitions and quantum spin dynamics. Here we demonstrate how such control can be implemented at the most fundamental level of a single spin at a specific site of an optical lattice. Using a tightly focused laser beam together with a microwave field, we were able to flip the spin of individual atoms in a Mott insulator with sub-diffraction-limited resolution, well below the lattice spacing. The Mott insulator provided us with a large two-dimensional array of perfectly arranged atoms, in which we created arbitrary spin patterns by sequentially addressing selected lattice sites after freezing out the atom distribution. We directly monitored the tunnelling quantum dynamics of single atoms in the lattice prepared along a single line, and observed that our addressing scheme leaves the atoms in the motional ground state. The results should enable studies of entropy transport and the quantum dynamics of spin impurities, the implementation of novel cooling schemes, and the engineering of quantum many-body phases and various quantum information processing applications.

The reliable detection of single quantum particles has revolutionized the field of quantum optics and quantum information processing. For several years, researchers have aspired to extend such detection possibilities to larger-scale, strongly correlated quantum systems in order to record in situ images of a quantum fluid in which each underlying quantum particle is detected. Here we report fluorescence imaging of strongly interacting bosonic Mott insulators in an optical lattice with single-atom and single-site resolution. From our images, we fully reconstruct the atom distribution on the lattice and identify individual excitations with high fidelity. A comparison of the radial density and variance distributions with theory provides a precise in situ temperature and entropy measurement from single images. We observe Mott-insulating plateaus with near-zero entropy and clearly resolve the high-entropy rings separating them, even though their width is of the order of just a single lattice site. Furthermore, we show how a Mott insulator melts with increasing temperature, owing to a proliferation of local defects. The ability to resolve individual lattice sites directly opens up new avenues for the manipulation, analysis and applications of strongly interacting quantum gases on a lattice. For example, one could introduce local perturbations or access regions of high entropy, a crucial requirement for the implementation of novel cooling schemes.

We investigate the response of two-dimensional pattern-forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above threshold is analyzed in terms of amplitude equations suggested for a 1:2 and 1:1 ratio between the wavelength of the spatial periodic forcing and the wavelength of the pattern of the respective system. Both sets of coupled amplitude equations are derived by a perturbative method from the Lengyel-Epstein model describing a chemical reaction showing Turing patterns, which gives us the opportunity to relate the generic response scenarios to a specific pattern-forming system. The nonlinear competition between stripe patterns and distorted hexagons is explored and their range of existence, stability, and coexistence is determined. Whereas without modulations hexagonal patterns are always preferred near onset of pattern formation, single-mode solutions (stripes) are favored close to threshold for modulation amplitudes beyond some critical value. Hence distorted hexagons only occur in a finite range of the control parameter and their interval of existence shrinks to zero with increasing values of the modulation amplitude. Furthermore, depending on the modulation amplitude, the transition between stripes and distorted hexagons is either subcritical or supercritical.